Self-duality triggered dynamical transition

Guarneri, Italo; Tian, Chushun; Wang, Jiao

doi:10.1103/physrevb.102.045433

Cited by 6 publications

(9 citation statements)

References 48 publications

(89 reference statements)

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“…Similar notions of dualities were suggested in systems ranging from self-assembled systems [10] to quantum rotors [11]. Rich consequences arise when a duality is combined with other constraints such as symmetries or conservation laws, ranging from degeneracies in the band structure [12][13][14] and topological states [15,16] to symmetries in the phonon response [17] and constraints on the stiffness tensor of an elastic medium [18].…”

Section: Introductionmentioning

confidence: 71%

Systematic generation of Hamiltonian families with dualities

Fruchart¹,

Yao²,

Vitelli³

2021

Preprint

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Dualities are hidden symmetries that map seemingly unrelated physical systems onto each other. The goal of this work is to systematically construct families of Hamiltonians endowed with a given duality and to provide a universal description of Hamiltonians families near self-dual points. We focus on tight-binding models (also known as coupled-mode theories), which provide an effective description of systems composed of coupled harmonic oscillators across physical domains. We start by considering the general case in which group-theoretical arguments suffice to construct families of Hamiltonians with dualities by combining irreducible representations of the duality operation in parameter space and in operator space. When additional constraints due to system specific features are present, a purely group theoretic approach is no longer sufficient. To overcome this complication, we reformulate the existence of a duality as a minimization problem which is amenable to standard optimization and numerical continuation algorithms. Combined with existing procedures to physically implement coupled-resonator Hamiltonians, our approach enables on demand design of photonic, mechanical, thermal, or electronic metamaterials with dualities.

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Section: Introductionmentioning

confidence: 71%

Systematic generation of Hamiltonian families with dualities

Fruchart¹,

Yao²,

Vitelli³

2021

Preprint

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“…Moreover, the phases encoded in these amplitudes have to be considered simultaneously to correctly trace the quantum evolution. (10)]. The green triangles, the red circles, and the blue squares are for the quantum results with j = 100, 200, and 400, respectively.…”

Section: B the Pseudoclassical Limit Of The Kicked Topmentioning

confidence: 99%

“…For the two cases close to the quantum resonance condition discussed in the previous section, we can see immediately how their linear entropy is related to that of the case β = δ based on the pseudoclassical analysis. First, for β = 2jπ + δ, from Equation (10), we have that [J γ (n; β)] 2 = [J γ (n; δ)] 2 at any time n; hence, S(n) must coincide with that for the system of β = δ throughout. However, for β = jπ + δ, from Equation ( 12), we know that γ [J γ (n; β)] 2 = γ [J γ (n; δ)] 2 only when mod (n, 8) = 0 or 4.…”

Section: The Dynamical Entanglementmentioning

confidence: 99%

“…After four decades of investigation, the richness of this paradigmatic model appears to be surprising. Far beyond quantum chaos, it has also been realized that this model may play a unique role in other fundamental problems, such as Anderson localization (transition) [ 4 , 5 , 6 , 7 ] and the quantum Hall effect [ 8 , 9 , 10 ]. Centering around the kicked rotor, an expanded overlapping field encompassing all these relevant problems is emerging [ 11 ].…”

Section: Introductionmentioning

confidence: 99%

“…The time dependence of the expected value of angular momentum Jx (a), Jy (b), and Jz (c), respectively, for α = 1 and β = 2jπ + 2. The black crosses are for the results by the pseudoclassical map [Eq (10)…”

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confidence: 99%

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Pseudoclassical Dynamics of the Kicked Top

Zou

Wang

2022

Entropy

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The kicked rotor and the kicked top are two paradigms of quantum chaos. The notions of quantum resonance and the pseudoclassical limit, developed in the study of the kicked rotor, have revealed an intriguing and unconventional aspect of classical–quantum correspondence. Here, we show that, by extending these notions to the kicked top, its rich dynamical behavior can be appreciated more thoroughly; of special interest is the entanglement entropy. In particular, the periodic synchronization between systems subject to different kicking strength can be conveniently understood and elaborated from the pseudoclassical perspective. The applicability of the suggested general pseudoclassical theory to the kicked rotor is also discussed.

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A string-theoretical analog of non-maximal chaos in some Sachdev-Ye-Kitaev-like models

Tian,

Ma,

Chen

2024

J. High Energ. Phys.

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Very recently two of the present authors have studied the chaos exponent of some Sachdev-Ye-Kitaev (SYK)-like models for arbitrary interaction strength [1]. These models carry supersymmetric (SUSY) or SUSY-like structures. Namely, bosons and Majorana fermions are both present and each of them interacts with (q − 1) particles, but the model is not necessarily supersymmetric. It was found that the chaos exponents in different models, no matter whether they carry SUSY(-like) structures or not, all follow a universal single-parameter scaling law for large q, and by tuning that parameter continuously a flow from maximally chaotic to completely regular motion results. Here we report a string-theoretical analog of this chaotic phenomenon. Specifically, we consider closed string scattering near the two-sided AdS black hole, whose amplitude grows exponentially in the Schwarzschild time, with a rate determined by the Regge spin of the Pomeron exchanged during string scattering. We calculate the Pomeron Regge spin for strings of different types, including the bosonic string, the type II superstring and the heterotic superstring. We find that the Pomeron Regge spin also displays a single-parameter scaling behavior independent of string types, with the parameter depending on the string length and the length scale characterizing the spacetime curvature; moreover, the scaling function has the same limiting behaviors as that for the chaos exponent of SYK-like models. Remarkably, the flow from maximally chaotic to completely regular motion in SYK-like models corresponds to the flow of the Pomeron Regge spin from 2 to 1.

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Self-duality triggered dynamical transition

Cited by 6 publications

References 48 publications

Systematic generation of Hamiltonian families with dualities

Systematic generation of Hamiltonian families with dualities

Pseudoclassical Dynamics of the Kicked Top

A string-theoretical analog of non-maximal chaos in some Sachdev-Ye-Kitaev-like models

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